1. (a) (b) The following complex electric field of a time-harmonic wave traveling in a source-free, free- space region is given by Ē = 5×10¯³ (4â¸ +3â²)e³(6y–8²) V/m. Assuming y and z represent their respective distances in meters, determine: The angle of wave travel (relative to the z axis). The phase constants of the wave along its direction of travel, the y axis, and the z axis (in radians per meter). The wavelengths of the wave along its direction of travel, the y axis, and the z axis (in meters). (c) (d) The frequency of the wave. (e) The phase velocities of the wave along the direction of travel, the y axis, and the z axis (in meters per second). (f) The associated magnetic field.

1. (a) (b) The following complex electric field of a time-harmonic wave traveling in a source-free, free- space region is given by Ē = 5×10¯³ (4â¸ +3â²)e³(6y–8²) V/m. Assuming y and z represent their respective distances in meters, determine: The angle of wave travel (relative to the z axis). The phase constants of the wave along its direction of travel, the y axis, and the z axis (in radians per meter). The wavelengths of the wave along its direction of travel, the y axis, and the z axis (in meters). (c) (d) The frequency of the wave. (e) The phase velocities of the wave along the direction of travel, the y axis, and the z axis (in meters per second). (f) The associated magnetic field.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

If the propagation speed of the wave is 1*10^7 m/s in a coaxial transmission line whose conductors are filled with dielectric material, what is the phase velocity of the wave in Mm/s (megameters/second)?
A homogeneous plane wave propagating in water in the positive z direction with an electric field of E = àx 200 cos (2,5.10°Tt) V/m at z = 0. The material constant of seawater is ɛr= 72, Hr = 1, and K = 4 s/m. Determine: a) Damping constant, phase constant and characteristic impedance! b) Distance, in which the amplitude is 5% of the amplitude at the point z = 0!
Q2/ A plane wave propagating through Lossy dielectric medium with &, = 8.4, = 2 " has E = 0.5 e-z/3 sin (10°t – Bz)ax v/m. Determine ß, loss tangent (condition), wave velocity and n? F H Mo 2 पत \1o +
Since the phase velocity of the wave in a coaxial transmission line whose conductors are filled with dielectric material is 1.5*10^7 m/s, what is the speed of the wave propagating in an unlimited dielectric medium, which has the same properties as the dielectric filling the guide, in Mm/s (megameters/second)?
(i) the wave period, T (ii) the wavelength, λ, (iii) the electric field, E. (iv) the phase difference between E and H
Problem 7: Light travels at a velocity of c = 3.0 × 108 m/s in a vacuum. Green light has a wavelength of λ = 535 nm Part (a) Input an expression for the frequency, ν, of green light. Part (b) What is the frequency in Hz? Part (c) How long does it take for the wave to make 3 full cycles in seconds?
The mathematical form of a wave packet formed by linear superposition of sinusoidal waves with constant amplitude A and wave numbers in the range k - Ak to k + A k is: rx + Ax S** а. y(x,t) = Acos (k't – o't) dk X- Ax b. rk+ Ak y(x,t) = / k - Ak Acos (k'x – w't) dk' w + A O c. y(x,t) = S** Acos (k'x – o't) do' ω-Δω O d. y(x,t) i+ At Acos (k'x – o't) dt' 1- At
Let ✰, ŷ be unit vectors in the positive x, y directions. A right-hand circular polarised wave travelling in the positive z direction has an electric field vector given by ER = Eox cos(kz - wt) + Eoŷ cos(kz − wt - πT " and a corresponding left-hand circular polarised wave, with an additional phase shift of 8, has an electric field vector given by П EL = Eox cos(kz - wt + d) + Eoŷ cos(kz - wt + +d). 2 Prove that the sum of these two circular polarised waves is equivalent to a single plane- polarised wave with its plane of polarisation at angle -8/2 from the x axis. (You may quote suitable trigonometric identities from the Appendix).
The electric field in a sinusoidal wave change asE = (25 N/C) cos[(1.2 x 10^11 rad/s)t + [(1.2 x 10^11 rad/s) x] Hint: The following relation might help: E = Emax cos[2p (t/T ± x/l)] and B = Bmax cos[2p (t/T ± x/l)] Clear show all the work and step to solve the problem. (a). In what direction does the wave propagate ? (b). What is the amplitude of the electric field oscillations ? (c). What is the amplitude of the magnetic field oscillations ? (d). What is the frequency of the wave ? (e). What is the wavelength ? (f). What is the speed? (g). What other information can you infer from the equation?
Problem 4: A traveling wave along the x-axis is given by the following wave functionψ(x, t) = 3.6 cos(1.4x - 9.2t + 0.34),where x in meter, t in seconds, and ψ in meters. Read off the appropriate quantities for this wave function and find the following characteristics of this plane wave: Part (a) The amplitude in meters. Part (b) The frequency, in hertz. Part (c) The wavelength in meters. Part (d) The wave speed, in meters per second. Part (e) The phase constant in radians.
Let us list some of the factors, which could possibly influence the speed of wave propagation:(i) nature of the source.(ii) direction of propagation.(iii) motion of the source and/or observer.(iv) wavelength.(v) intensity of the wave. On which of these factors, if any, does(a) the speed of light in vacuum,(b) the speed of light in a medium (say, glass or water), depend?
The speed of electromagnetic waves (which include visible light, radio, and x rays) in vacuum is 3.0 * 10^8 m/s. (a)Wavelengths of visible light waves range from about 400 nm in the violet to about 700 nm in the red.What is the range of frequencies of these waves? (b) The range of frequencies for shortwave radio (for example, FM radio and VHF television) is 1.5 to 300 MHz.What is the corresponding wavelength range? (c) X-ray wavelengths range from about 5.0 nm to about 1.0 * 10-2 nm.What is the frequency range for x rays?